PYTHAGOREAN THEOREM FOR RIGHT TRIANGLES

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PYTHAGOREAN THEOREMFORRIGHT TRIANGLES
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Teacher Page

• Content Mathematics
• Grade Level 6-10
• Creator Sharon Stadler
• This activity addresses Missouri Standards

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What is the Pythagorean Theorem?

• It is a formula.
• It is the rule for solving right triangles.
• It helps us classify a triangle if we know the
  lengths of its three sides.

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The Formula

• a 2 b 2 c 2

Hypotenuse c
Leg a
Leg b
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Solve Right Triangles

• If you know two of the measurements in a right
  triangle, then you can use the formula to
  calculate the third measurement.

Find the missing length of side b.
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Use the formula

• a 2 b 2 c 2

15 in
b
12 in

144 in2 b 2 225 in2
b2 225-144
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• Continuing to solve using the formula

144 in2 b 2 225 in2
b 2 225-144
b 2 81
b 9 in
The length of the other leg is 9 inches.
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Solve another right triangle

• The two legs of a right triangle are 20 yards and
  26 yards. Find the length of the hypotenuse to
  the nearest tenth.

Use a2 b2 c2
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• a2 b2 c2

c
202 262 c2
20
400 676 c2
26
1076 c2
c 32.8 yd
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TAKE A SHORT CUT

• Angela was in a hurry to get home and ran
  diagonally across the church yard instead of
  following the side- walk. How many meters
  shorter was her short cut?

16 m
?
25 m
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25m
Find the length of the diagonal (the short
cut). (16m)2 (25m)2
16m
25m
256m2 625m2 881m2
C 881m2 about 30 meters
The long route is 16m 25m , or 41 meters.
Angelas short cut was 11 meters shorter.
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Wheres Home?

• Matthew and his friends hiked 4 miles west, 2
  miles north, 1 mile east, and 2 more miles north.
  How far would they have to hike back to camp if
  they could go in a straight line?
• Draw and label a diagram that represents the
  path.
• Provide work for answer.

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Wheres Home?

• Matthew and his friends are 3 miles west and 4
  miles north of camp.
• 32 42
• 9 16
• 25

camp
25 5 mi
4 mi